Vol. 9, No. 3, 2016

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Generalized factorization in $\mathbb{Z}/m\mathbb{Z}$

Austin Mahlum and Christopher Park Mooney

Vol. 9 (2016), No. 3, 379–393

Generalized factorization theory for integral domains was initiated by D. D. Anderson and A. Frazier in 2011 and has received considerable attention in recent years. There has been significant progress made in studying the relation τn for the integers in previous undergraduate and graduate research projects. In 2013, the second author extended the general theory of factorization to commutative rings with zero-divisors. In this paper, we consider the same relation τn over the modular integers, m. We are particularly interested in which choices of m,n yield a ring which satisfies the various τn-atomicity properties. In certain circumstances, we are able to say more about these τn-finite factorization properties of m.

modular integers, generalized factorization, zero-divisors, commutative rings
Mathematical Subject Classification 2010
Primary: 13A05, 13E99, 13F15
Received: 27 September 2014
Revised: 7 April 2015
Accepted: 6 June 2015
Published: 3 June 2016

Communicated by Vadim Ponomarenko
Austin Mahlum
Department of Mathematics
Viterbo University
La Crosse, WI 54601
United States
Christopher Park Mooney
Department of Mathematics
Westminster College
Fulton, MO 65251
United States